Double-hybrid Density Functional Theory Methods Research Articles

Limiting factors in the accuracy of DFT calculation for redox potentials.

In the present study, we have investigated factors affecting the accuracy of computational chemistry calculation of redox potentials, namely the gas-phase ionization energy (IE) and electron affinity (EA), and the continuum solvation effect. In general, double-hybrid density functional theory methods yield IEs and EAs that are on average within ~0.1 eV of our high-level W3X-L benchmark, with the best performing method being DSD-BLYP/ma-def2-QZVPP. For lower-cost methods, the average errors are ~0.2-0.3 eV, with ωB97X-3c being the most accurate (~0.15 eV). For the solvation component, essentially all methods have an average error of ~0.3 eV, which shows the limitation of the continuum solvation model. Curiously, the directly calculated redox potentials show errors of ~0.3 eV for all methods. These errors are notably smaller than what can be expected from error propagation with the two components (IE and EA, and solvation effect). Such a discrepancy can be attributed to the cancellation of errors, with the lowest-cost GFN2-xTB method benefiting the most, and the most accurate ωB97X-3c method benefiting the least. For organometallic species, the redox potentials show large deviations exceeding ~0.5 eV even for DSD-BLYP. The large errors are attributed to those for the gas-phase IEs and EAs, which represents a major barrier to the accurate calculation of redox potentials for such systems.

Estimating the Vertical Ionization Potential of Single-Stranded DNA Molecules

The electronic properties of DNA molecules, defined by the sequence-dependent ionization potentials of nucleobases, enable long-range charge transport along the DNA stacks. This has been linked to a range of key physiological processes in the cells and to the triggering of nucleobase substitutions, some of which may cause diseases. To gain molecular-level understanding of the sequence dependence of these phenomena, we estimated the vertical ionization potential (vIP) of all possible nucleobase stacks in B-conformation, containing one to four Gua, Ade, Thy, Cyt, or methylated Cyt. To do this, we used quantum chemistry calculations and more precisely the second-order Møller-Plesset perturbation theory (MP2) and three double-hybrid density functional theory methods, combined with several basis sets for describing atomic orbitals. The calculated vIP of single nucleobases were compared to experimental data and those of nucleobase pairs, triplets, and quadruplets, to observed mutability frequencies in the human genome, reported to be correlated with vIP values. This comparison selected MP2 with the 6-31G* basis set as the best of the tested calculation levels. These results were exploited to set up a recursive model, called vIPer, which estimates the vIP of all possible single-stranded DNA sequences of any length based on the calculated vIPs of overlapping quadruplets. vIPer's vIP values correlate well with oxidation potentials measured by cyclic voltammetry and activities obtained through photoinduced DNA cleavage experiments, further validating our approach. vIPer is freely available on the github.com/3BioCompBio/vIPer repository.

Do Double-Hybrid Exchange-Correlation Functionals Provide Accurate Chemical Shifts? A Benchmark Assessment for Proton NMR.

A benchmark density functional theory (DFT) study of 1H NMR chemical shifts for data sets comprising 200 chemical shifts, including complex natural products, has been carried out to assess the performance of DFT methods. Two new benchmark data sets, NMRH33 and NMRH148, have been established. The meta-GGA revTPSS performs remarkably well against the NMRH33 benchmark set (mean absolute deviation (MAD), 0.10 ppm; maximum deviation (max), 0.26 ppm) with the smallest MAD of all evaluated functionals. The best-performing double-hybrid density functional (DHDF), revDSD-BLYP (MAD, 0.16 ppm; max, 0.35 ppm), performs similarly to hybrid-GGA methods (e.g., mPW1PW91/6-311G(d) (MAD, 0.15 ppm; max, 0.36 ppm)), but at a considerably higher computational cost. The results indicate that currently available double-hybrid DFT methods offer no benefit over GGA (including hybrid and meta) functionals in the calculation of 1H NMR chemical shifts.

Kinetics and Thermodynamics of Reactions Involving Criegee Intermediates: An Assessment of Density Functional Theory and Ab Initio Methods Through Comparison with CCSDT(Q)/CBS Data.

Reactions involving Criegee intermediates (CIs, R1 R2 COO) are important in atmospheric ozonolysis models. In recent years, density functional theory (DFT) and CCSD(T)-based ab initio methods are increasingly being used for modeling reaction profiles involving CIs. We obtain highly accurate CCSDT(Q)/CBS reaction energies and barrier heights for ring-closing reactions involving atmospherically important CIs (R1 /R2 = H, Me, OH, OMe, F, CN, cyclopropene, ethylene, acetaldehyde, and acrolein). We use this benchmark data to evaluate the performance of DFT, double-hybrid DFT (DHDFT), and ab initio methods for the kinetics and thermodynamics of these reactions. We find that reaction energies are more challenging for approximate theoretical procedures than barrier heights. Overall, taking both reaction energies and barrier heights into account, only one of the 58 considered DFT methods (the meta-GGA MN12-L) attains near chemical accuracy, with root-mean-square deviations (RMSDs) of 3.5 (barrier heights) and 4.7 (reaction energies) kJ mol-1 . Therefore, MN12-L is recommended for investigations where CCSD(T)-based methods are not computationally feasible. For reaction barrier heights performance does not strictly follow Jacob's Ladder, for example, DHDFT methods do not perform better than conventional DFT methods. Of the ab initio methods, the cost-effective CCSD(T)/CBS(MP2) approach gives the best performance for both reaction energies and barrier heights, with RMSDs of 1.7 and 1.4 kJ mol-1 , respectively. All the considered Gaussian-n methods show good performance with RMSDs below the threshold of chemical accuracy for both reaction energies and barrier heights, where G4(MP2) shows the best overall performance with RMSDs of 2.9 and 1.5 kJ mol-1 , respectively. © 2019 Wiley Periodicals, Inc.

The Lowest-Energy Isomer of C2Si2H4 Is a Bridged Ring: Reinterpretation of the Spectroscopic Data Based on DFT and Coupled-Cluster Calculations

The lowest-energy isomer of C 2 Si 2 H 4 is determined by high-accuracy ab initio calculations to be the bridged four-membered ring 1,2-didehydro-1,3-disilabicyclo[1.1.0]butane (1), contrary to prior theoretical and experimental studies favoring the three-member ring silylsilacyclopropenylidene (2). These and eight other low-lying minima on the potential energy surface are characterized and ordered by energy using the CCSD(T) method with complete basis set extrapolation, and the resulting benchmark-quality set of relative isomer energies is used to evaluate the performance of several comparatively inexpensive approaches based on many-body perturbation theory and density functional theory (DFT). Double-hybrid DFT methods are found to provide an exceptional balance of accuracy and efficiency for energy-ordering isomers. Free energy profiles are developed to reason the relatively large abundance of isomer 2 observed in previous measurements. Infrared spectra and photolysis reaction mechanisms are modeled for isomers 1 and 2, providing additional insight about previously reported spectra and photoisomerization channels.

A quantum chemical study of the effect of substituents in governing the strength of the S–F bonds of sulfenyl-type fluorides toward homolytic dissociation and fluorine atom transfer

The gas-phase homolytic S–F bond dissociation energies (BDEs) of 21 sulfenyl-type fluorides (RSF) have been obtained using the W1w thermochemical protocol. The BDEs (at 298 K) for the species in this set range from 316.2 (HCCSF) to 368.1 (H2CCHSF) kJ mol–1. We additionally report fluorine-transfer energies (FTEs), corresponding to the energetics of fluorine transfer from RSF to H2S. At 298 K, the FTEs range from –10.7 (H2AlSF) to 90.7 (MeHNSF) kJ mol–1. We have also assessed the performance of a wide range of density functional theory (DFT) and double-hybrid DFT methods (in conjunction with the A'VQZ basis set) for the calculation of these quantities. For the calculation of S–F BDEs, the M06-2X procedure offers the best performance, with a mean absolute deviation (MAD) of 1.6 kJ mol–1, whilst for the FTEs, B2K-PLYP and DSD-PBEP86 offer the best performance with MADs of 0.5 kJ mol–1.

A computational foray into the mechanism and catalysis of the adduct formation reaction of guanine with crotonaldehyde.

Crotonaldehyde, a common environmental pollutant and product of endogenous lipid peroxidation, reacts with guanine to form DNA adducts with pronounced genotoxicity and mutagenicity. Here, we explore the molecular mechanism of this adduct formation using double-hybrid density functional theory methods. The reaction can be envisaged to occur in a two-step fashion via an aza-Michael addition leading to an intermediate ring-open adduct followed by a cyclization reaction giving the mutagenic ring-closed adduct. We find that (i) a 1,2-type addition is favored over a 1,4-type addition for the aza-Michael addition, and (ii) an initial tautomerization of the guanine moiety in the resulting ring-open adduct significantly reduces the barrier toward cyclization compared to the direct cyclization of the ring-open adduct in its keto-form. Overall, the aza-Michael addition is found to be rate-determining. We further find that participation of a catalytic water molecule significantly reduces the energy barriers of both the addition and cyclization reaction. © 2018 Wiley Periodicals, Inc.

Can Popular DFT Approximations and Truncated Coupled Cluster Theory Describe the Potential Energy Surface of the Beryllium Dimer?

The potential energy surface (PES) of the ground state of the beryllium dimer poses a significant challenge for high-level ab initio electronic structure methods. Here, we present a systematic study of basis set effects over the entire PES of Be2 calculated at the full configuration interaction (FCI) level. The reference PES is calculated at the valence FCI/cc-pV{5,6}Z level of theory. We find that the FCI/cc-pV{T,Q}Z basis set extrapolation reproduces the shape of the FCI/cc-pV{5,6}Z PES as well as the binding energy and vibrational transition frequencies to within ~10 cm−1. We also use the FCI/cc-pV{5,6}Z PES to evaluate the performance of truncated coupled cluster methods (CCSD, CCSD(T), CCSDT, and CCSDT(Q)) and contemporary density functional theory methods (DFT) methods for the entire PES of Be2. Of the truncated coupled cluster methods, CCSDT(Q)/cc-pV{5,6}Z provides a good representation of the FCI/cc-pV{5,6}Z PES. The GGA functionals, as well as the HGGA and HMGGA functionals with low percentages of exact exchange tend to severely overbind the Be2 dimer, whereas BH&HLYP and M06-HF tend to underbind it. Range-separated DFT functionals tend to underbind the dimer. Double-hybrid DFT functionals show surprisingly good performance, with DSD-PBEP86 being the best performer. Møller–Plesset perturbation theory converges smoothly up to fourth order; however, fifth-order corrections have practically no effect on the PES.

W4-17: A diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods.

Atomization reactions are among the most challenging tests for electronic structure methods. We use the first-principles Weizmann-4 (W4) computational thermochemistry protocol to generate the W4-17 dataset of 200 total atomization energies (TAEs) with 3σ confidence intervals of 1 kJmol-1 . W4-17 is an extension of the earlier W4-11 dataset; it includes first- and second-row molecules and radicals with up to eight non-hydrogen atoms. These cover a broad spectrum of bonding situations and multireference character, and as such are an excellent benchmark for the parameterization and validation of highly accurate ab initio methods (e.g., CCSD(T) composite procedures) and double-hybrid density functional theory (DHDFT) methods. The W4-17 dataset contains two subsets (i) a non-multireference subset of 183 systems characterized by dynamical or moderate nondynamical correlation effects (denoted W4-17-nonMR) and (ii) a highly multireference subset of 17 systems (W4-17-MR). We use these databases to evaluate the performance of a wide range of CCSD(T) composite procedures (e.g., G4, G4(MP2), G4(MP2)-6X, ROG4(MP2)-6X, CBS-QB3, ROCBS-QB3, CBS-APNO, ccCA-PS3, W1, W2, W1-F12, W2-F12, W1X-1, and W2X) and DHDFT methods (e.g., B2-PLYP, B2GP-PLYP, B2K-PLYP, DSD-BLYP, DSD-PBEP86, PWPB95, ωB97X-2(LP), and ωB97X-2(TQZ)). © 2017 Wiley Periodicals, Inc.

Assessment of Contemporary Theoretical Methods for Bond Dissociation Enthalpies

The density functional theory (DFT) is the most popular method for evaluating bond dissociation enthalpies (BDEs) of most molecules. Thus, we are committed to looking for alternative methods that can balance the computational cost and higher precision to the best for large systems. The performance of DFT, double-hybrid DFT, and high-level composite methods are examined. The tested sets contain monocyclic and polycyclic aromatic molecules, branched hydrocarbons, small inorganic molecules, etc. The results show that the mPW2PLYP and G4MP2 methods achieve reasonable agreement with the benchmark values for most tested molecules, and the mean absolute deviations are 2.43 and 1.96 kcal/mol after excluding the BDEs of branched hydrocarbons. We recommend the G4MP2 is the most appropriate method for small systems (atoms number≤20); the double-hybrid DFT methods are advised for large aromatic molecules in medium size (20≤atoms number≤50), and the double-hybrid DFT methods with empirical dispersion correction are recommended for long-chain and branched hydrocarbons in the same size scope; the DFT methods are advised to apply for large systems (atoms number≥50), and the M06-2X and B3P86 methods are also favorable. Moreover, the differences of optimized geometry of different methods are discussed and the effects of basis sets for various methods are investigated.

Frequency Scale Factors for Some Double-Hybrid Density Functional Theory Procedures: Accurate Thermochemical Components for High-Level Composite Protocols

In the present study, we have obtained geometries and frequency scale factors for a number of double-hybrid density functional theory (DH-DFT) procedures. We have evaluated their performance for obtaining thermochemical quantities [zero-point vibrational energies (ZPVE) and thermal corrections for 298 K enthalpies (ΔH298) and 298 K entropies (S298)] to be used within high-level composite protocols (using the W2X procedure as a probe). We find that, in comparison with the previously prescribed protocol for optimization and frequency calculations (B3-LYP/cc-pVTZ+d), the use of contemporary DH-DFT methods such as DuT-D3 and DSD-type procedures leads to a slight overall improved performance compared with B3-LYP. A major strength of this approach, however, lies in the better robustness of the DH-DFT methods in that the largest deviations are notably smaller than those for B3-LYP. In general, the specific choices of the DH-DFT procedure and the associated basis set do not drastically change the performance. Nonetheless, we find that the DSD-PBE-P86/aug'-cc-pVTZ+d combination has a very slight edge over the others that we have examined, and we recommend its general use for geometry optimization and vibrational frequency calculations, in particular within high-level composite methods such as the higher-level members of the WnX series of protocols. The scale factors determined for DSD-PBE-P86/aug'-cc-pVTZ+d are 0.9830 (ZPVE), 0.9876 (ΔH298), and 0.9923 (S298).

A dataset of homolytic C–Cl bond dissociation energies obtained by means of W1w theory

Abstract We herein report a dataset of 28 homolytic C–Cl bond dissociation energies (BDEs) (to be known as the CCl28 dataset), obtained using the benchmark-quality W1w thermochemical protocol. This set contains chlorinated organic molecules that consist of either sp 3 -, sp 2 - or sp -hybridized C–Cl bonds. The species in this set have C–Cl BDEs (at 298 K) that differ by as much as 168.4 kJ mol –1 , with allyl chloride having the lowest BDE (291.7 kJ mol –1 ) and 1-chloroprop-1-yne having the largest (460.1 kJ mol –1 ). Given the benchmark quality of the CCl28 dataset, it may serve as a useful reference for assessing the performance of more approximate quantum chemical methods, such as density functional theory (DFT) and double-hybrid DFT methods.

On the inclusion of post-MP2 contributions to double-hybrid density functionals.

In this study, we explore the effect of supplementing the DuT spin-component-scaled double-hybrid density functional method with post-second-order Møller-Plesset-type theory (MP2) correlation terms. We find that the inclusion of additional MP3 correlation energies has almost no effect on the performance. Further addition of correlation effects from MP4 generally leads to a small improvement in the performance. However, we find that the inclusion of the higher-order perturbative correlation effects does not rectify some major shortcomings of DuT for more challenging systems, and the use of MP4, in fact, leads to a significant deterioration in the performance in some cases. We also find that the use of correlation energies from CCSD(T) instead of those from MP3 and MP4 does not lead to a substantial improvement over the MP4-based method, both in general and in some difficult cases that we have examined. An additional observation is that, for large systems that are dominated by noncovalent interactions, DuT and the two MPn-based post-MP2 double-hybrid density functional theory (DFT) procedures all benefit from the inclusion of dispersion corrections. Overall, our investigation suggests that the current generation of MP2-based double-hybrid DFT methods may already be providing close to the optimal performance that can be achieved with the double-hybrid methodology paired with spin-component-scaling. Development of even better double hybrids is an active research field, and we hope that our study provides valuable insights. We recommend the continuing use of existing MP2-based double-hybrid methods as a bridging level between hybrid density functional procedures and high-level wave-function-based procedures.

Obtaining Good Performance With Triple-ζ-Type Basis Sets in Double-Hybrid Density Functional Theory Procedures.

A variety of combinations of B-LYP-based double-hybrid density functional theory (DHDFT) procedures and basis sets have been examined. A general observation is that the optimal combination of exchange contributions is in the proximity of 30% Becke 1988 (B88) exchange and 70% Hartree-Fock (HF) exchange, while for the correlation contributions, the use of independently optimized spin-component-scaled Møller-Plesset second-order perturbation theory (SCS-MP2) parameters (MP2OS and MP2SS) is beneficial. The triple-ζ Dunning aug'-cc-pVTZ+d and Pople 6-311+G(3df,2p)+d basis sets are found to be cost-effective for DHDFT methods. As a result, we have formulated the DuT-D3 DHDFT procedure, which employs the aug'-cc-pVTZ+d basis set and includes 30% B88 and 70% HF exchange energies, 59% LYP, 47% MP2OS, and 36% MP2SS correlation energies, and a D3 dispersion correction with the parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.35. Likewise, the PoT-D3 DHDFT procedure was formulated with the 6-311+G(3df,2p)+d basis set and has 32% B88 and 68% HF exchange energies, 63% LYP, 46% MP2OS, and 27% MP2SS correlation energies, and the D3 parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.30. Testing using the large E3 set of 740 energies demonstrates the robustness of these methods. Further comparisons show that the performance of these methods, particularly DuT-D3, compares favorably with the previously reported DSD-B-LYP and DSD-B-LYP-D3 methods used in conjunction with quadruple-ζ aug'-pc3+d and aug'-def2-QZVP basis sets but at lower computational expense. The previously reported ωB97X-(LP)/6-311++G(3df,3pd) procedure also performs very well. Our findings highlight the cost-effectiveness of appropriate- and moderate-sized triple-ζ basis sets in the application of DHDFT procedures.